Problem: Nauuo is a girl who loves playing chess.

One day she invented a game by herself which needs n chess pieces to play on a m× m chessboard. The rows and columns are numbered from 1 to m. We denote a cell on the intersection of the r-th row and c-th column as (r,c).

The game's goal is to place n chess pieces numbered from 1 to n on the chessboard, the i-th piece lies on (r_i,\,c_i), while the following rule is satisfied: for all pairs of pieces i and j, |r_i-r_j|+|c_i-c_j|≥|i-j|. Here |x| means the absolute value of x.

However, Nauuo discovered that sometimes she couldn't find a solution because the chessboard was too small.

She wants to find the smallest chessboard on which she can put n pieces according to the rules.

She also wonders how to place the pieces on such a chessboard. Can you help her?

Input

The only line contains a single integer n (1≤ n≤ 1000) — the number of chess pieces for the game.

Output

The first line contains a single integer — the minimum value of m, where m is the length of sides of the suitable chessboard.

The i-th of the next n lines contains two integers r_i and c_i (1≤ r_i,c_i≤ m) — the coordinates of the i-th chess piece.

If there are multiple answers, print any.

Examples

Input


2


Output


2
1 1
1 2

Input


4


Output


3
1 1
1 3
3 1
3 3

Note

In the first example, you can't place the two pieces on a 1×1 chessboard without breaking the rule. But you can place two pieces on a 2×2 chessboard like this:

<image>

In the second example, you can't place four pieces on a 2×2 chessboard without breaking the rule. For example, if you place the pieces like this:

<image>

then |r_1-r_3|+|c_1-c_3|=|1-2|+|1-1|=1, |1-3|=2, 1<2; and |r_1-r_4|+|c_1-c_4|=|1-2|+|1-2|=2, |1-4|=3, 2<3. It doesn't satisfy the rule.

However, on a 3×3 chessboard, you can place four pieces like this:

<image>

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.awt.Point;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author caoash
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastScanner in = new FastScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        BNauuoAndChess solver = new BNauuoAndChess();
        solver.solve(1, in, out);
        out.close();
    }

    static class BNauuoAndChess {
        static int n;
        static ArrayList<Point> points;

        public void solve(int testNumber, FastScanner br, PrintWriter pw) {
            n = br.nextInt();
            points = new ArrayList<>();
            int lo = 0;
            int hi = 1000;
            int ans = 0;
            while (lo <= hi) {
                int mid = (lo + hi) / 2;
                if (works(mid)) {
                    hi = mid - 1;
                    ans = mid;
                } else {
                    lo = mid + 1;
                }
            }
            pw.println(ans);
            points.clear();
            int x = 1;
            int y = 1;
            for (int d = 0; d < n; d++) {
                if (d % 2 == 0) {
                    int v = (d / 2);
                    points.add(new Point(x + v, y + v));
                } else {
                    int v1 = (d / 2);
                    int v2 = (d / 2) + 1;
                    points.add(new Point(x + v1, y + v2));
                }
            }
            for (Point p : points) {
                pw.println(p.x + " " + p.y);
            }
        }

        public static boolean works(int mid) {
            points.clear();
            int x = 1;
            int y = 1;
            for (int d = 0; d < n; d++) {
                if (d % 2 == 0) {
                    int v = (d / 2);
                    if (x + v > mid || y + v > mid) {
                        return false;
                    }
                    points.add(new Point(x + v, y + v));
                } else {
                    int v1 = (d / 2);
                    int v2 = (d / 2) + 1;
                    if (x + v1 > mid || y + v2 > mid) {
                        return false;
                    }
                    points.add(new Point(x + v1, y + v2));
                }
            }
            return true;
        }

    }

    static class FastScanner {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private FastScanner.SpaceCharFilter filter;

        public FastScanner(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}